For each reductive algebraic group G, we introduce and study unipotent bicrystals which serve as a regular version of birational geometric and unipotent crystals introduced earlier by the authors. The framework of unipotent bicrystals allows, on the one hand, to study systematically such varieties as Bruhat cells in G and their convolution products and, on the other hand, to give a new construction of many normal Kashiwara crystals including those for G∨-modules, where G∨ is the Langlands dual… CONTINUE READING